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On a backward problem for fractional diffusion equation with Riemann-Liouville derivative |
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| Authors: | Nguyen Huy Tuan Nguyen Hoang Tuan Dumitru Baleanu Tran Ngoc Thach |
| Institution: | 1. Institute of Research and Development, Duy Tan University, Da Nang, 550000 Vietnam;2. School of Medicine, Vietnam National University HCMC, Ho Chi Minh City, Vietnam;3. Department of Mathematics, Cankaya University, Ankara, 06530 Turkey;4. Applied Analysis Research Group, Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam |
| Abstract: | In the present paper, we study the initial inverse problem (backward problem) for a two-dimensional fractional differential equation with Riemann-Liouville derivative. Our model is considered in the random noise of the given data. We show that our problem is not well-posed in the sense of Hadamard. A truncated method is used to construct an approximate function for the solution (called the regularized solution). Furthermore, the error estimate of the regularized solution in L2 and Hτ norms is considered and illustrated by numerical example. |
| Keywords: | backward problem fractional diffusion equation random noise regularized solution |